Certainly not in the same way that I can own a pen or a nice wristwatch. Now we're getting somewhere! So what does it mean to "own" a company?
If the company is just me and a bag of tools, fixing people's cars on their driveway, do I own that company? What does it even mean for me to "own" it?
You're making a good argument to point out that 'ownership' takes a lot of different forms. And an interest in one class of thing isn't the same as others. Ownership comes with differing, restrictions, rights, and responsibilities depending on the thing.
An opinion of mine the ownership of a company through stocks is secondary to stocks being a quasi-cash financial instrument like bonds.
What does that mean? You don’t “own” the company, do you?